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Existence of Weak Solutions in Wasserstein Space for a Chemotaxis Model Coupled to FluidEquations
Kang, Kyungkeun,Kim, Hwa Kil Society for Industrial and Applied Mathematics 2017 SIAM journal on mathematical analysis Vol.49 No.4
<P>We consider a coupled system of Keller--Segel-type equations and theincompressible Navier--Stokes equations in spatial dimension two andthree. We first establish the existence of a weak solution of a Fokker--Plankequation in the Wasserstein space under the assumption that initial massis integrable and has finite entropy. As a result, we construct solutionsof Keller--Segel--Navier--Stokes equations such that the density of biologicalorganism belongs to the absolutely continuous curves in the Wasserstein space,in the case that its initial mass is assumed to be bounded and integrable.</P>
On the behaviour of Navier–Stokes equations near a possible singular point
Kang, Kyungkeun,Lee, Jihoon Institute of Physics and the London Mathematical S 2010 Nonlinearity Vol.23 No.12
<P>We show that if a singularity of suitable weak solutions to Navier–Stokes equations occurs, then either <I>p</I> or at least two of ∂<SUB><I>i</I></SUB><I>v</I><SUB><I>i</I></SUB>, <I>i</I> = 1, 2, 3, have neither upper bounds nor lower bounds in any neighbourhood of the singularity. In the case of axially symmetric solutions, we prove that either <I>p</I> or ∂<SUB><I>r</I></SUB><I>v</I><SUP><I>r</I></SUP> is not bounded both below and above near a singular point, if it exists.</P>
Regularity criteria of Magenetohydrodynamic equations in domains with boundaries
Kyungkeun Kang,Jae-Myoung Kim 한국산업응용수학회 2011 한국산업응용수학회 학술대회 논문집 Vol.6 No.2
We study three dimensional incompressible magnetohydrodynamic equations in either bounded domains or a half-space when no-slip or slip boundary conditions for velocity fields and slip boundary conditions for magnetic fields are considered. We present new regularity criteria of weak solutions: a weak solution, (u, b), becomes regular if u satisfies Serrin’s type conditions. In addition, in case of a half-space, we demonstrate that if tangential components of velocity fields and normal component of magnetic fields satisfy Serrin’s type conditions, then weak solutions become regular.
Elliptic systems with measurable coefficients of the type of Lamé system in three dimensions
Kang, Kyungkeun,Kim, Seick Elsevier 2011 Journal of differential equations Vol.251 No.9
<P><B>Abstract</B></P><P>We study the 3×3 elliptic systems ∇(a(x)∇×u)−∇(b(x)∇⋅u)=f, where the coefficients a(x) and b(x) are positive scalar functions that are measurable and bounded away from zero and infinity. We prove that weak solutions of the above system are Hölder continuous under some minimal conditions on the inhomogeneous term <I>f</I>. We also present some applications and discuss several related topics including estimates of the Greenʼs functions and the heat kernels of the above systems.</P>
Kang, Kyungkeun,Miura, Hideyuki,Tsai, Tai-Peng Elsevier 2018 Advances in mathematics Vol.323 No.-
<P><B>Abstract</B></P> <P>We derive refined estimates of the Green tensor of the stationary Stokes system in the half space. We then investigate the spatial asymptotics of stationary solutions of the incompressible Navier–Stokes equations in the half space. We also discuss the asymptotics of fast decaying flows in the whole space and exterior domains. In the Appendix we consider axisymmetric self-similar solutions.</P>
강병도(Byungdo Kang),이호상(Hosang Lee),박경석(Kyoungsuk Park),조경근(Kyungkeun Cho),홍승준(Seungjun Hong) 한국자동차공학회 2007 한국자동차공학회 춘 추계 학술대회 논문집 Vol.- No.-
In this study, eye-recovery time after glare exposure to oncoming headlight was measured increasing illuminance at eye point with various light sources(H4, H7 and HID) and aiming conditions. for measuring eye-recovery time, experimental setup was made up in dark room and used various twelve illumination conditions of light sources and aiming conditions. Different light sources were exposed at subjects for 4 seconds to test people's eye. In case of target of 400% ratio of contrast, it was found that under nominal aiming condition the glare exposures representing halogen and HID bulbs produced similar recovery time. However, with 0.5° of misaim upwards, non-standard HID bulb exposure produced significantly longer recovery time. It showed that total braking distance of car using non-standard bulbs were increased about 27.5m at driving with 80㎞/h.